In this paper, a proton exchange membrane fuel cell (PEMFC) is implemented as a grid-connected electrical generator that uses hydrogen gas as fuel and air as an oxidant to produce electricity through electrochemical reactions. Analysis demonstrated that the performance of the PEMFC greatly depends on the rate of fuel supply and air supply pressure. Critical fuel and air supply pressures of the PEMFC are analysed to test its feasibility for the grid connection. Air and fuel supply pressures are varied to observe the effects on the PEMFC characteristics, efficiency, fuel supply, and air consumption over time. The PEMFC model is then implemented into an electrical power system with the aid of power electronics applications. Detailed mathematical modelling of the PEMFC is discussed with justification. The PEMFC functions as an electrical generator that is connected to the local grid through a power converter and a transformer. Modulation of the converter is controlled by means of a proportional-integral controller. The two-axis control methodology is applied to the current control of the system. The output voltage waveform and control actions of the controller on the current and frequency of the proposed system are plotted as well. Simulation results show that the PEMFC performs efficiently under certain air and fuel pressures, and it can effectively supply electrical power to the grid.